STATISTICS

Course Credits: 3 Units

Prerequisites: Math 114 and Stat 123

← Go Back

STAT 129 - Regression and Correlation Analysis

Course Description

Linear regression model; model selection; regression diagnostics; use of dummy variables; remedial measures.

Course Learning Outcomes

After completion of the course, the student should be able to:

  1. Develop linear regression models
  2. Perform inferences in regression analysis
  3. Assess the aptness of the models
  4. Check and test model assumptions
  5. Perform remedial measures to improve model fit
  6. Explain and interpret final models appropriately
Course Outline

UNIT 1. Introduction

  1. Regression Models
  2. Uses of Regression Analysis
  3. Applications of Regression Analysis
  4. Data for Regression Analysis
  5. Steps in Regression Analysis

UNIT 2. Simple Linear Regression

  1. Simple Linear Regression Model with Distribution of Error Terms Unspecified
  2. Estimation of Regression Function
  3. Estimation of Error Terms Variance σ²
  4. Normal Error Regression Model

UNIT 3. Inferences in Regression Analysis

  1. Inferences Concerning β0 and β1
  2. Interval Estimation of E(Yh)
  3. Prediction of New Observation
  4. Confidence Band for Regression Line
  5. ANOVA Approach to Regression Analysis
  6. Coefficient of Determination and Correlation

UNIT 4. Regression Diagnostics and Remedial Measures

  1. Diagnostics for Predictor Variable
  2. Residuals and Residual Analysis
  3. F Test for Lack of Fit
  4. Remedial Measures and Transformations
  5. Exploration of Shapes of Regression Function

UNIT 5. Simultaneous Inferences and Other Topics

  1. Joint Estimation of β0 and β1
  2. Simultaneous Estimation of Mean Responses
  3. Simultaneous Prediction Intervals for New Observations
  4. Other Topics
    • Regression through the Origin
    • Effects of Measurement Errors
    • Inverse Predictions
    • Choice of X Levels

Unit 6. Matrix Approach to Simple Linear Regression Analysis

  1. Matrices and their Properties
  2. Simple Linear Regression Model in Matrix Terms
  3. Least Squares Estimation of Regression Parameters
  4. ANOVA Results and Inferences in Regression Analysis
  5. Estimation of Mean Response and Prediction of New Observations

Unit 7. Multiple Linear Regression

  1. General Linear Regression Model in Matrix Terms
  2. Inferences about Regression Parameters
  3. Extra Sum of Squares and Its Uses
  4. Diagnostics and Remedial Measures
  5. Multicollinearity and Its Effects

Unit 8. Regression Models for Quantitative and Qualitative Predictors

  1. Polynomial Regression Models
  2. Interaction Regression Models
  3. Qualitative Predictors
  4. Modelling Interactions between Quantitative and Qualitative Predictors
  5. Comparison of Two or More Regression Functions

Unit 9. Model Building, Diagnostics, and Remedial Measures for MLR Models

  1. The Model-Building Strategy
  2. Selection of Independent Variables
  3. Automatic Search Procedures for Model Selection
  4. Model Validation